Vacuum insulated structures have many practical uses and can be constructed as described, for example, in U.S. Pat. Nos. 7,681,299 and 7,374,063, in which tube walls and jacket walls are vacuum brazed together to create a strong metallurgical joint that has a higher melting temperature than the braze material itself. Typically, the tube walls and the outer jacket walls of such vacuum insulated structures are quite thin, often less than about 0.010″ inches. Consequently, it can be difficult to affix a fitting onto a vacuum insulated structure to enable the structure to be mounted or supported by an external device. In particular, an attempt to weld or solder a fitting to a tube wall or the outer jacket wall of the structure risks perforating the thin wall and destroying the vacuum seal. Additionally, acid that is commonly contained in solder materials can erode into and eventually perforate the thin outer jacket wall. Further, the thin walls of the vacuum insulated structure may not be capable of supporting a threaded or compression-type fitting without sustaining damage.